
// Make newform 6024.2.a.p in Magma, downloaded from the LMFDB on 09 May 2024.
// To make the character of type GrpDrchElt, type "MakeCharacter_6024_a();"
// To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
// To make the newform (type ModFrm), type "MakeNewformModFrm_6024_2_a_p();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6024_2_a_p();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function ConvertToHeckeField(input: pass_field := false, Kf := [])
    if not pass_field then
        poly := [-3364, -22140, -13761, 67298, 10892, -53458, -1300, 17652, -863, -2796, 280, 210, -29, -6, 1];
        Kf := NumberField(Polynomial([elt : elt in poly]));
        AssignNames(~Kf, ["nu"]);
    end if;
    Rf_num := [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-6, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-56474950, -253959291, -52788358, 933220260, 59731310, -726563800, -38974970, 207665199, 9438328, -26472460, -869644, 1553117, 26892, -34385], [543511258, 5250877601, 7501423177, -14580166089, -9653543531, 10740423537, 4526703895, -3245410102, -921011508, 470527080, 81418106, -32877251, -2582249, 891500], [-2060172338, -15515835721, -10547722286, 38536651212, 16436289310, -28100462208, -8770496906, 8476711133, 1920505680, -1224526764, -177040372, 85005175, 5763184, -2285707], [-677427348, -3691152442, -2259965299, 9440736513, 3566414523, -6827363977, -1865943851, 2026352809, 402727860, -286607520, -36738588, 19439080, 1185871, -510731], [1930586878, 11780644049, 7029931060, -30232129854, -11158864646, 22294893624, 6055282684, -6714256819, -1341558738, 961333458, 124543394, -65938241, -4072364, 1750919], [-636577414, -4904604035, -4982795950, 13368961119, 6716846546, -9973980471, -3303220780, 3020215300, 693826704, -434576058, -62535530, 29958653, 2007980, -799400], [2458464146, 16722285277, 17130259784, -45888598104, -22949713318, 34072151028, 11083245044, -10278303353, -2300026932, 1473998214, 205940440, -101245663, -6588652, 2690857], [-798333708, -6272928610, -6578394766, 17847143889, 8801355990, -13473230383, -4337434292, 4096485739, 913528686, -590411514, -82526094, 40709620, 2654776, -1085369], [1300892340, 9075081374, 7318586177, -23897723349, -10334058561, 17571182555, 5240205949, -5266901315, -1119757014, 751000860, 101829564, -51337298, -3285059, 1359385], [1560309976, 10105957332, 8209065926, -25553159163, -11564497352, 18422349217, 5699815236, -5472245579, -1192572510, 776737884, 107080910, -52961826, -3427662, 1400227], [-6511648574, -43344239917, -36259637984, 113289156915, 51662191384, -83439350505, -26089480472, 25099371248, 5552233938, -3595411272, -503783854, 247008691, 16236166, -6572812]];
    Rf_basisdens := [1, 1, 1, 10615128, 47768076, 95536152, 15922692, 47768076, 15922692, 47768076, 15922692, 15922692, 15922692, 47768076];
    Rf_basisnums := ChangeUniverse([[z : z in elt] : elt in Rf_num], Kf);
    Rfbasis := [Rf_basisnums[i]/Rf_basisdens[i] : i in [1..Degree(Kf)]];
    inp_vec := Vector(Rfbasis)*ChangeRing(Transpose(Matrix([[elt : elt in row] : row in input])),Kf);
    return Eltseq(inp_vec);
end function;


// To make the character of type GrpDrchElt, type "MakeCharacter_6024_a();"
function MakeCharacter_6024_a()
    N := 6024;
    order := 1;
    char_gens := [4519, 3013, 2009, 4273];
    v := [1, 1, 1, 1];
    // chi(gens[i]) = zeta^v[i]
    assert UnitGenerators(DirichletGroup(N)) eq char_gens;
    F := CyclotomicField(order);
    chi := DirichletCharacterFromValuesOnUnitGenerators(DirichletGroup(N,F),[F|F.1^e:e in v]);
    return MinimalBaseRingCharacter(chi);
end function;

function MakeCharacter_6024_a_Hecke(Kf)
    return MakeCharacter_6024_a();
end function;


function ExtendMultiplicatively(weight, aps, character)
    prec := NextPrime(NthPrime(#aps)) - 1; // we will able to figure out a_0 ... a_prec
    primes := PrimesUpTo(prec);
    prime_powers := primes;
    assert #primes eq #aps;
    log_prec := Floor(Log(prec)/Log(2)); // prec < 2^(log_prec+1)
    F := Universe(aps);
    FXY<X, Y> := PolynomialRing(F, 2);
    // 1/(1 - a_p T + p^(weight - 1) * char(p) T^2) = 1 + a_p T + a_{p^2} T^2 + ...
    R<T> := PowerSeriesRing(FXY : Precision := log_prec + 1);
    recursion := Coefficients(1/(1 - X*T + Y*T^2));
    coeffs := [F!0: i in [1..(prec+1)]];
    coeffs[1] := 1; //a_1
    for i := 1 to #primes do
        p := primes[i];
        coeffs[p] := aps[i];
        b := p^(weight - 1) * F!character(p);
        r := 2;
        p_power := p * p;
        //deals with powers of p
        while p_power le prec do
            Append(~prime_powers, p_power);
            coeffs[p_power] := Evaluate(recursion[r + 1], [aps[i], b]);
            p_power *:= p;
            r +:= 1;
        end while;    
    end for;
    Sort(~prime_powers);
    for pp in prime_powers do
        for k := 1 to Floor(prec/pp) do
            if GCD(k, pp) eq 1 then
                coeffs[pp*k] := coeffs[pp]*coeffs[k];
            end if;
        end for;
    end for;
    return coeffs;
end function;


function qexpCoeffs()
    // To make the coeffs of the qexp of the newform in the Hecke field type "qexpCoeffs();"
    weight := 2;
    raw_aps := [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, -1, 1, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0], [1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -1, 0, -1, -1, 0, -1, 0, 0], [0, 1, -1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0], [2, 0, 0, 0, -1, 0, 0, -1, -1, -1, 0, 0, 0, 0], [0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [1, 0, 0, -1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 1], [0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, -1, 0], [0, 0, 0, 0, -1, 0, 0, 0, 0, 1, 0, 0, 0, -1], [1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0], [-3, 0, 0, 1, 1, 1, -1, 1, -1, -1, 0, -1, 0, 1], [2, -1, 1, 1, 0, 1, 0, 0, 1, -1, 1, -1, -1, -1], [1, 1, -1, 0, -1, 0, 0, 1, 1, 0, 0, 1, 0, 1], [-1, 0, 0, 2, -1, 0, 0, 1, 0, 1, -1, 0, 1, 1], [0, 1, -1, 1, -1, -1, -1, 1, 1, 0, 0, 0, 0, 0], [1, 1, -1, 1, -2, -1, 0, 0, -1, 1, 0, 1, 1, 2], [1, 1, -1, -2, 1, 0, -1, 1, 1, -1, 0, 0, -1, -2], [2, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0], [2, 1, -1, -1, 0, -1, 1, 1, 1, 0, -1, 1, 1, 1], [-2, 0, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 1], [3, 1, 0, -1, -1, -1, 1, 0, 2, 2, -1, 0, -1, -1], [1, -1, 1, 1, 1, 1, -1, 1, 0, 0, 1, -2, 0, 0], [0, 0, 1, -1, 0, -1, 0, -1, 0, -1, -1, 0, -1, -1], [1, 0, 0, -1, 0, -1, 1, 0, 0, 1, -1, 0, 1, 1], [3, -1, -1, 2, 0, 1, 0, 1, 1, -2, 0, 0, 1, 1], [-1, 1, 1, 0, -1, 0, -2, -1, -1, 0, -1, -1, 0, 0], [5, -2, 1, 0, -1, 0, 1, 1, 0, 1, -3, 0, 0, -2], [4, -1, 0, -2, 1, -1, 2, 0, 1, 1, -2, 0, 0, 0], [1, 0, 1, 0, 0, 2, -1, 1, 0, -1, -1, -1, 0, -2], [1, 0, 0, -3, 1, 1, 0, 0, 2, 0, -1, 0, -1, -2], [3, -1, -1, 0, 0, 2, -1, 1, 0, -1, 0, 0, 1, 1], [4, 0, -1, -3, 1, -1, 1, 0, 1, 2, 0, 2, -1, 0], [3, 1, -1, -1, -1, -1, 1, -2, -1, 1, -2, 1, 3, 1], [5, 0, 2, 1, -1, 1, 1, 0, -1, 1, 0, 0, 1, 0], [2, 0, -2, 2, -2, -2, -1, 1, 0, -1, 0, 0, 0, 2], [5, -1, -1, 0, 1, 0, 2, -1, 3, 1, 1, 1, 0, 0], [9, -1, -1, 0, -3, -2, 0, 0, -1, 1, -3, 1, 0, 1], [2, 1, -2, 0, -1, -2, 1, -1, -1, -1, -1, 1, 1, 2], [2, 0, -2, -1, -1, -1, -1, -1, -2, -1, -2, 0, 0, 1], [2, -2, -1, 0, 1, -1, 1, 2, 2, 1, -2, 0, 0, 1], [-1, -1, 1, -3, 3, 1, 0, -1, 1, -1, 0, 0, 0, 0], [-1, -1, 2, 2, -1, 0, 1, -1, -1, 1, 0, 0, 0, 2], [7, -2, -2, 1, -1, -1, 0, -1, 0, 0, 2, 0, -1, 1], [1, -2, -2, 1, 2, 1, -1, 2, -1, -2, 0, -1, 0, 1], [1, -1, -1, 2, 0, -2, 1, -2, -2, 0, 2, 1, 0, 2], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [6, 0, 0, 1, -1, 0, -1, 1, -1, 0, -1, -1, 1, 1], [2, 0, 0, -3, 2, -1, -1, 2, 1, 0, 1, -1, -2, -2], [6, -4, 0, -3, 3, 2, -1, 0, 2, -3, 0, 0, -3, -3], [3, -2, 0, -1, 0, 1, 0, 0, 2, 0, 0, -1, -3, 0], [4, 1, -1, 0, -2, 0, -1, -2, -1, 2, 0, 1, -1, 0], [9, 2, 0, -4, 2, 1, -1, 0, 1, 1, 1, 1, -3, -2], [0, -1, 1, 1, 0, 2, 1, 0, 0, 1, -1, 2, 3, 0], [6, -4, 2, 1, 3, 4, -2, 2, -1, -2, 1, -4, 0, -2], [1, 1, 1, 2, -5, 0, -1, -3, -2, 0, 0, 0, 0, 0], [4, 3, -2, 0, -4, 0, -1, 0, -2, 1, -1, 4, 1, 0], [6, -1, 1, 2, -1, 2, -1, -1, 0, -1, 1, -2, 0, -1], [9, -1, -2, 1, -1, -1, -1, 2, 1, 0, -1, 0, 2, 1], [1, 3, 1, 2, -4, -2, 1, -1, -1, 2, -1, 0, 3, 1], [-1, -3, 1, 2, 2, 4, -1, 2, 1, 0, 0, 1, 1, 0], [-2, 4, 0, -4, 0, -2, 0, -2, 1, 0, 0, -2, -1, 0], [2, 1, -1, 1, -1, -3, -1, 0, -2, 1, -4, 0, 2, 2], [7, 1, 1, 1, 0, 0, 0, -3, 1, 0, 4, 0, 1, 1], [3, 3, 0, -3, -1, -1, 0, -6, -3, 3, 1, 2, 0, 0], [0, -3, -1, -1, 3, 0, 1, 3, 2, 2, -2, 0, 0, 0], [-1, 0, 2, -3, 3, 1, -2, -1, 2, -2, 5, -3, -3, -1], [-4, 1, 3, -2, 3, 0, 2, -1, -1, -1, 2, -2, 1, 2], [3, 1, 1, 0, -4, 0, 1, -3, -2, 0, 0, 1, 0, 0], [5, -4, -2, -1, 4, 1, 1, 3, 1, -2, -1, -2, 1, 1], [3, 3, 0, -3, -1, 1, 0, 4, 1, -1, -2, 0, 4, 0], [10, 2, -2, 1, 1, -1, 0, 4, 1, 0, 0, 0, 0, 3], [3, 2, -2, -2, -2, 0, -1, 0, 2, 1, 0, 3, 1, -3], [0, 0, -2, 4, -3, -2, 2, 2, 0, 0, -2, 1, 1, 2], [7, 0, -3, -1, -3, 1, -1, 0, -1, -2, -2, 2, 1, -1], [7, -2, -1, 1, -4, -3, 3, -7, -2, 0, -1, 0, 0, 2], [4, -3, 1, 1, 4, 3, -1, 3, 2, -2, 5, -1, -2, -1], [2, 1, 2, 3, -5, 0, -1, -1, -3, 1, -2, -1, 3, 1], [-4, 5, -1, 0, 0, 2, -3, 4, 2, 0, -1, 0, -1, -3], [4, -2, 0, 1, 1, -1, 2, -4, -1, -3, 2, -1, -1, 0], [-3, 2, -2, 2, 0, -2, 2, 2, 0, -2, 1, 0, 2, 5], [14, -2, -2, -3, -3, -3, 2, -2, 4, 4, 0, 4, -1, 1], [-4, -1, 3, -1, 1, 3, 2, 0, 1, -1, 1, 3, -2, -2], [0, 1, 1, -1, 4, 3, -3, 2, 0, 0, 0, -2, -5, -5], [6, 0, -2, -2, 0, 0, 1, 0, -1, 1, -5, 0, 3, 1], [-4, -1, -2, 2, 1, 3, -3, 0, -2, -1, 1, -2, 1, 1], [-5, 5, -1, -4, 2, -2, 0, -2, 0, 0, 5, 1, -3, -1], [-4, -2, 2, -3, 5, 4, -2, 2, 2, -3, 1, -1, -2, -3], [0, -1, -2, 3, 2, -1, 0, 4, 3, 0, 0, -1, -1, 2], [4, -1, 1, 0, 4, 2, 2, 2, 4, 0, 1, -2, -1, -2], [9, -2, 2, -1, 4, 5, -2, 4, -1, -2, 1, -3, -1, -4], [1, 3, 1, -1, -3, 1, -1, 1, 2, -2, 1, -1, -2, -1], [-2, -3, -1, 3, -1, -1, 0, 4, 1, -1, -2, 0, 4, 2], [5, -2, 2, 3, 1, 3, 1, 2, 3, 3, -3, 1, 2, 0], [1, 1, -3, 0, 2, -2, -1, -1, 3, 0, 0, 2, 0, 1], [2, 3, -1, 3, 0, 1, 2, 3, 3, 3, 0, 3, 2, 2], [6, 4, 0, -4, -1, -4, 2, -2, 1, 2, -1, 2, 0, -1], [1, 0, -2, -2, 0, -2, 6, 2, 4, 1, 0, 5, 2, 2], [-2, -8, 2, 7, 0, 1, 0, 2, -1, 2, 1, -3, 1, 2], [2, -1, 3, 0, 2, 4, -2, -1, -2, -1, -3, -2, 2, -2], [9, -1, -1, 0, -2, 0, 0, 3, 2, 0, 2, 0, -1, -2], [-3, 3, 3, -3, 1, 1, -1, -1, -2, -1, 2, -2, -2, 0], [3, -2, 2, -3, 3, -3, 1, 1, -2, -1, -3, -3, 0, 1], [0, -2, 2, 3, -1, 1, 0, -2, -4, -4, -1, -1, 0, 0], [-1, -6, 1, 2, 2, 2, 4, 1, 2, 2, 0, 2, 1, 0], [2, 2, 4, -1, 1, 3, 2, -1, 0, 0, -5, -1, 2, -3], [7, 0, -4, 1, -2, -1, -1, 1, -2, -2, 0, 0, 1, 1], [4, 1, 2, -1, -5, -2, 1, -5, -3, 0, 2, 0, 2, -2], [9, 3, -3, -2, 3, 0, -3, 4, 2, -1, -1, 2, -1, -1], [-7, 5, -3, -2, 3, -5, -1, 2, 2, -1, 2, 1, -1, 3], [0, -3, -3, -2, 3, -2, 1, -2, -5, -4, 0, -1, 2, 3], [5, -3, 1, -1, -1, -2, 4, -6, -1, 1, 1, 2, 1, 1], [-6, 6, 0, 1, -3, -5, -2, 0, -4, 3, -2, 1, 1, 4], [-4, 0, 0, -1, 0, 3, -2, 2, 2, -3, 0, 1, -1, -1], [-8, 3, 1, -3, 2, -3, -1, -5, -5, -1, 3, -2, -2, 2], [2, 0, 1, 3, 1, -1, 3, 0, -1, 3, 0, 0, 3, 2], [-5, 1, 1, 0, 2, 0, 2, 1, 2, 3, 0, -2, -3, -2], [0, 2, 2, -4, 1, 2, -1, 4, -1, -3, -1, 0, -1, -2], [-4, 2, 2, 1, 1, 4, -3, 0, -1, -4, 2, 2, -2, 1], [-2, -1, 5, 0, 4, -2, 1, 0, 1, 3, -1, -4, -3, -2], [-5, 1, -2, 3, -1, 1, -2, 4, -1, -3, -4, 2, 1, -1], [-6, -1, 1, -2, 3, 0, 4, 0, 0, 2, 2, 1, 1, 2], [-10, 3, 1, 0, 4, 2, -2, 0, -3, 0, 3, -1, -3, -3], [2, -3, 5, -1, -2, -1, 2, -3, -1, 6, -2, 0, 1, -3], [3, 2, -1, 0, 4, 0, 1, 0, -1, -1, 0, 0, 1, 5], [1, 6, 4, -4, -5, -2, 1, -4, -2, 0, -2, 1, 2, 0], [-8, -4, 0, 0, 0, 2, -3, 1, 0, -3, 1, -3, -1, -3], [6, 4, 2, -3, -1, -4, 1, -7, -4, 1, 1, -1, -2, -3], [-5, -1, -1, 1, -3, -3, 2, 0, -5, 2, -4, 2, 4, 6], [3, -3, 1, -1, -6, 1, -4, 3, -2, 1, -4, 0, 1, -4], [-1, -3, -3, 4, 1, 2, 0, 3, -2, -2, -3, -1, 3, 2], [-3, 0, -2, 0, 3, 2, -2, 6, 2, 0, -1, -2, -3, 0], [5, 1, -1, -3, -2, 0, 4, -1, -3, -3, -2, 1, 2, 2], [4, -4, 0, 0, 1, 4, 2, 2, 4, 2, 4, -1, 1, -2], [-9, -2, -2, 0, 4, 0, 1, -2, 0, 1, 1, 1, -3, 1], [2, -4, -1, 1, 3, 0, 3, 3, 1, 3, -1, 0, 1, 0], [-4, -4, -2, 0, 6, -6, 5, 2, 2, 1, 1, 0, 1, 4], [8, -2, -4, -1, -2, -3, 3, 2, 2, -2, -3, 2, 2, 3], [-3, 1, 0, 0, 3, -2, 2, 4, -2, -2, 1, 0, -1, 6], [-5, -5, -1, 0, -2, 2, 3, -4, 3, 2, -4, 6, -2, -2], [5, -3, -1, 1, 1, 1, 0, 6, 4, -2, -4, -3, 2, 1], [-11, 1, -3, -2, -3, 0, -1, -1, 0, 2, 3, 3, -2, -3], [2, 0, -1, -5, 4, -1, 1, 4, 1, 0, 2, 2, -3, 2], [-14, 1, 3, -4, -4, 0, 0, -5, -1, 0, -2, 3, -2, -5], [6, -6, 2, -1, -1, 0, 2, -3, -3, -1, 0, -3, -1, -2], [-14, 0, -2, 1, -1, 0, -2, -3, -5, 2, 4, -3, 1, 2], [2, 8, -2, -5, 1, -3, -1, -5, -1, 1, 0, 2, 0, 1], [-9, 6, 0, 1, -4, -7, -2, -2, -3, 4, 2, -1, 1, 0], [1, 2, -2, 3, -2, -1, -1, 1, 3, 5, 3, 2, 1, 3], [0, -2, 0, 0, 1, 0, -5, -1, 2, -4, 2, -6, -5, -3], [11, 4, -2, -4, -2, -3, 5, 0, 4, 3, -3, 7, 2, 0], [-12, -4, 0, 10, 0, 6, -5, 5, -1, -4, 2, -5, 2, -1], [-2, 5, 1, -4, 1, -1, 0, -5, -2, -3, 3, -3, -1, 4], [3, -3, 3, 1, 5, 3, 0, -1, 4, -1, -2, -2, -5, -2], [6, 2, 0, 5, -9, -2, -1, -3, -4, 1, -1, -2, 1, 0], [0, 0, -4, -6, 2, -6, 3, 1, -2, 3, 3, 3, -3, 1], [3, -6, 4, 0, 2, 2, 0, -1, 0, -1, 0, -6, 1, -3], [4, 6, -4, -5, 1, -4, 1, -1, 0, 1, -3, 4, 1, 2], [3, -4, 6, 2, 5, 2, -1, -3, 0, -3, 9, -7, -2, -3], [0, 2, -1, 2, -3, 1, -1, 5, 2, 1, -1, 2, 0, 0], [-5, 0, -3, -2, 2, -2, 2, -1, 4, -2, 2, 2, -5, 4], [-5, -9, -3, 4, 4, 4, -1, 8, 3, -1, -2, -2, -2, 0], [-7, -2, -3, -1, -2, -5, 2, -2, -3, -1, -1, -2, 4, 3], [-5, 3, 1, 2, -5, 2, 1, -7, -5, -6, 0, 3, 0, 1], [3, 2, -6, -3, -3, -5, 4, 3, 3, 6, -3, 5, 0, 5], [1, 4, 4, 2, 4, 4, -2, 4, 5, 1, 6, 2, -1, -3], [-10, 5, 1, -3, 4, 3, -2, -1, -2, 1, 0, 0, 1, 1], [5, -1, -1, 2, -2, 2, -4, 1, 3, -1, -2, -1, 1, 3], [-7, -6, 2, 6, 3, 0, 1, -4, 0, 0, 5, -2, -1, 1], [3, -6, -2, 2, -2, 1, -4, 2, -5, -1, -4, 1, 2, 1], [11, -1, 3, -4, 2, 0, -3, 3, 2, 0, -4, -2, 1, -5], [-4, 0, 0, 1, -2, 1, -6, 2, -6, -7, -2, 0, 2, 0], [10, 2, 0, 6, -9, -4, 1, -4, -4, 1, -6, -1, 3, 0], [0, 1, 3, -5, 2, 1, 1, -6, -2, 0, 1, 3, 0, 0], [2, -9, -1, -3, -4, -1, 4, -3, 4, 3, 2, 4, -3, -1], [-12, -3, -5, 0, 0, 0, -2, 2, -1, -2, 4, 1, 2, 2], [6, 2, 0, -5, 2, 5, 1, 3, 2, 2, 3, 2, -2, -4], [0, -1, 3, 1, 0, 3, 0, 1, 1, 0, 4, 3, 3, 0], [8, -3, 0, -1, 0, 3, -2, -1, 3, 2, -1, 0, -3, -1], [0, -3, -1, 1, -1, -1, 1, -2, 0, 1, 3, -3, 0, -2], [-5, -8, -2, 0, 2, 0, 1, 1, 2, 2, -2, 2, -1, 3], [-14, 6, 0, -3, 7, 3, -3, 1, 6, -2, 4, 3, -2, -1], [8, -6, -2, 2, -3, -2, -3, 2, -3, 2, -3, -2, 4, 0], [-6, -3, 3, -3, 1, -1, 1, -4, -2, -8, 3, -2, -1, -2], [-12, -5, -3, 2, 0, 4, -4, -1, 3, 1, 0, 0, -3, 3], [-9, 1, -1, 4, -1, 3, 0, 0, -2, -2, 7, -1, 1, 2], [9, -2, 0, 6, -7, 1, -1, -2, -4, 2, -7, 1, 6, -1], [-10, -3, -1, -6, 6, 2, -2, 0, -2, -5, 3, 1, -3, 3], [-4, 10, -4, -10, 3, -4, -1, -3, 3, -3, 5, 5, -3, 2], [-3, -1, 1, 1, 3, -3, 4, 5, 5, 2, 0, -3, 0, 1], [0, 1, 1, 4, -4, 2, 1, 7, 3, 5, -6, 0, 5, -1], [-5, -7, 3, -1, 5, 3, 1, -2, 5, 1, 1, -2, -8, -5], [2, -3, -2, 2, 2, -2, 0, 3, -1, 2, -2, -1, 2, 0], [-11, 8, -1, -1, -1, 3, -2, -1, -1, 1, 6, 3, 2, -4], [10, -1, -1, -2, -3, 2, -2, -1, 3, -2, -1, 5, 4, 1], [-8, -5, 1, 1, 0, -3, 5, -4, 0, 6, 1, -1, -2, 0], [-4, 1, 5, 4, 0, 2, 2, 0, 2, -1, 1, 1, 0, 0], [-13, 1, 1, -6, 4, -2, 2, 2, 2, -1, 7, -1, 1, 3], [-2, 0, 3, 1, 4, -3, -1, -2, -1, -4, 2, -3, -1, 0], [4, 8, -3, 1, -4, -2, -4, 6, -1, -2, -5, -1, 5, 2], [-2, -2, -4, -8, -4, -4, 4, -6, -1, 1, 0, 3, -1, 2], [-13, 7, 1, 0, 2, -1, -2, 0, -2, 3, 5, -1, -3, -5], [-5, -2, 0, -8, 3, -4, 3, 0, 0, 1, 3, -1, -5, -2], [-10, -5, -3, 3, -2, -1, -4, 0, -3, -3, 1, 0, 4, 2], [0, 2, 2, 1, -3, -1, 4, 1, -4, 3, -5, 0, 7, -2], [3, 4, 0, -1, 0, 5, -3, -3, -2, -3, -4, 2, 0, 1], [4, -4, -4, 1, -4, 3, 1, 3, -1, 1, -3, -3, 3, 0], [10, 1, 7, -2, 3, 2, 3, -3, 6, 3, 4, -2, -5, -8], [-13, 4, 2, -1, 1, -1, -4, 0, 0, -3, 4, -3, 0, -4], [-4, 2, -6, 4, -1, -1, 1, 4, 1, -3, -2, -1, 3, 2], [-1, 1, 1, 0, 8, -2, 3, -3, -1, 4, 9, -1, -3, 2], [-8, -2, -3, 1, -1, -1, 1, -2, -2, -1, 1, 7, -1, -1], [-12, 6, -1, -1, 2, -3, -4, 0, -3, -8, 1, -2, -2, 2], [-9, -1, -2, 2, -7, -4, 2, -10, -1, 1, 0, -3, 1, 1], [9, -5, 1, -2, 6, 4, -2, 5, 8, 3, -4, -1, 0, -5], [-7, -2, 2, 3, 4, 5, 0, 3, -4, -7, -1, -2, 0, -2], [0, -2, -5, 2, 8, 1, -2, 6, 7, 1, -1, -2, 0, 3], [-4, 0, 0, 2, -2, 0, -1, 4, 0, 3, -5, 3, 1, 0], [4, -1, 1, 1, 6, 5, -4, 5, 3, 1, -5, -4, 2, -5], [-1, 0, -2, 3, -6, 0, -1, -1, -2, 3, 0, 4, -1, 0], [-9, 2, -2, -4, -5, -4, 4, -3, -4, 0, -2, 1, 6, 4], [14, 1, -1, -1, 0, 5, 2, -2, -4, 1, -4, 6, 5, 2], [3, -6, 2, -2, 7, 4, 3, 3, 10, -1, 0, -2, -1, -2], [-3, 3, -3, -7, -6, -5, 3, -1, -4, 4, -3, 1, -1, 1], [6, -5, 1, -2, 4, 4, 1, 2, -3, -3, -2, -1, 0, -2], [6, 2, -5, 2, 0, -5, 1, -1, 0, 3, -1, 2, -1, 5], [11, 1, -1, 8, -1, -2, 5, 6, 3, 1, -3, -3, 3, 2], [-17, -2, 0, 3, -5, 0, -3, 2, -1, -5, -5, -1, 1, 1], [-2, -4, 5, 4, 3, 2, 0, -3, -3, 0, 4, -4, -6, -3], [0, 7, 3, 2, -5, -2, 1, -5, 2, -2, -5, 2, 0, 1], [-3, -3, 7, 2, -2, 5, 4, -4, 3, -6, 3, 0, -2, -4], [-12, 6, 4, -6, 1, -2, 0, -11, 2, -2, 1, 1, -5, -5], [9, -6, 3, -7, 3, -1, 0, -9, -6, -6, 3, -6, -6, -5], [0, 4, 4, -2, 6, 2, 0, 1, 2, 2, 1, -3, 0, -7], [-5, 2, -4, 0, -1, 4, 0, 5, 5, 3, -3, 6, 0, 1], [8, 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-1, -3, 4, 3, -2, -1, 3], [-5, -6, -5, 1, 3, 3, -2, 3, 6, -7, 0, -2, -4, -5], [11, 5, -2, -3, -1, -1, 4, -6, 3, 4, 8, 9, -3, -3], [15, -3, 5, 5, -3, -2, 6, -2, 3, 8, -7, 0, 6, 3], [4, 9, 5, -1, 0, 8, -5, 1, 7, -4, 0, 1, -3, -6], [13, -4, -2, 3, -4, 0, 0, 3, 7, 0, 3, 2, 1, -1], [8, -1, 7, 4, 1, 3, 1, 1, 2, -3, 0, -3, 3, -5], [-17, 0, 2, -1, 0, -5, 3, 0, -4, 3, -3, -4, 3, 0], [4, 4, 0, -2, -5, -2, 3, 4, 0, 3, -1, 2, 9, 0], [14, -3, 7, -3, 1, 7, -3, -3, -5, -1, -5, -2, 3, -3], [6, 4, 4, -6, 12, 0, 1, 1, 7, 2, 0, -5, -5, -5], [-8, -1, 1, 2, 3, 6, 0, 10, 9, -1, -5, -4, 1, -1], [-4, 0, 4, -4, 5, 0, 5, 1, -4, -4, 0, -6, -3, 1], [-2, -3, -1, 2, -11, -4, 7, -4, 0, -2, -5, 4, 5, 6], [0, 4, -3, -5, 0, 2, 3, -5, -2, 2, 3, 7, -2, -2], [6, 2, 2, 4, -6, -4, 0, 1, -5, 0, -9, -3, 8, 4], [19, 3, 0, -1, 6, 7, -5, 8, 3, -3, -7, 0, 5, -2], [-1, -3, -3, -3, -2, -5, 7, 1, 6, 2, -4, 7, 4, 4], [2, 2, 4, -3, 9, 1, 0, 2, 0, -5, 2, -6, -5, 3], [9, 2, 5, -2, -7, -4, 4, -3, -3, 1, -4, 0, 0, 2], [19, 7, -7, 0, -6, -2, -1, 1, 2, 3, -4, 6, -1, 1], [-2, -5, -5, 3, -4, 1, 0, 7, -3, -3, -4, 2, 6, 3], [14, 6, -8, -3, 0, -3, -7, 4, 1, -2, -5, 1, 0, 0], [-5, 3, -3, 2, -2, 2, -3, -3, -4, -1, 1, 6, 3, 1], [-3, -1, 4, 2, 3, 8, -3, 3, 4, 0, -5, -5, 0, -3], [-5, 2, 2, -5, -3, -1, 1, -2, -8, -2, -2, 6, -3, -1], [10, 2, -2, 0, -4, 3, 4, 9, 9, 3, -10, 6, 3, -4], [21, 1, 3, 2, 0, 4, -3, -3, 4, -5, 4, -4, 1, 1], [15, -2, 0, 3, 0, -1, -5, 4, -5, -4, -4, -7, 1, 5], [13, 0, 3, -4, -4, 0, -5, -9, -4, -6, 1, -5, -2, -4], [-12, -3, -1, 2, 8, 4, -5, -2, -3, -2, 2, -1, -4, 4], [3, -3, -1, -3, 3, 5, -2, 8, 8, -2, -5, -1, 1, -5], [-4, 5, 3, 0, 6, -2, -3, 5, 0, 0, 0, 1, -1, 0], [7, -1, -8, -2, 5, -2, 3, 6, 1, 4, 7, 5, 1, 2], [8, -3, -2, -1, 1, -3, 2, 3, 4, -2, -1, 1, 2, 3], [11, 2, 8, 1, 2, -1, 1, -5, -8, 2, -1, -2, 0, -3], [-1, -7, -1, 5, -3, 4, -3, -8, -11, -2, 2, 1, 0, 1], [-20, -12, 8, 3, 10, 5, 2, -1, -1, -5, 2, -5, -2, -2], [14, 1, -1, -1, 4, -4, -1, -2, 0, 2, 7, 0, 3, 2], [-11, 6, 0, 10, -4, 4, -3, 3, 1, 0, 1, -4, 1, 1], [5, -5, -1, 2, -1, -6, 10, -1, 3, 9, -6, 7, 8, 4], [4, 0, 4, 4, 5, 5, 2, 3, 1, -4, -2, 0, 2, -1], [-4, -13, 1, 5, 8, 3, 2, 7, 10, 0, -4, -8, -1, 1], [3, -6, 2, 2, -3, -2, 1, 0, -4, 3, -5, -5, 4, 0], [-13, -8, -2, 3, 3, 9, -9, 3, 0, -6, 0, -2, -3, 1], [4, 9, -9, -2, -8, 0, -2, 9, 3, -1, -12, 9, 6, 0], [9, -4, 2, -1, -3, 3, -1, -6, -8, -6, -3, -4, 2, 2], [-4, 5, 3, -4, 11, 6, -1, 1, 7, 1, 0, 0, -6, 0], [-13, -11, 3, 0, 7, 6, -1, 0, 5, 2, 4, 0, -2, -2], [-10, -1, -3, 0, 1, -6, 2, -1, 1, 5, -8, 6, -5, -2], [-1, 2, 6, 0, 1, 1, -3, -2, 0, -4, -3, -5, 0, -1], [10, 6, 6, -4, -1, -4, 1, -1, -4, 3, -3, 1, 0, 4], [-4, 8, -8, -9, -5, -9, 4, -6, -5, 4, -6, 5, 3, 4], [-11, 2, 1, 1, 3, -1, 2, 0, 0, 0, -8, 0, -2, -2], [6, -3, 1, 2, -2, -4, 4, -1, -1, 6, 1, 5, -4, -1], [-5, -3, 1, 5, -9, 7, -5, -5, -1, 2, -3, 1, -5, -8], [9, -8, -3, 5, -2, -1, 0, -7, -2, -1, 4, 1, 1, 4], [-8, -3, -5, -9, 5, -1, 2, 9, 3, 0, 0, 4, -3, -1], [15, 1, 3, -5, 3, -3, 6, -2, 3, 6, 1, -1, 0, -1], [35, -5, -9, -8, 4, -2, 0, 7, 4, -1, -6, 3, 2, -1], [-11, -1, 1, -6, -5, -6, 1, -6, -2, -2, -1, -3, -3, 0], [-12, -1, 7, -1, 0, 2, -2, -3, -13, -4, 1, 2, 4, 2], [-3, 6, 0, 1, 2, 1, 0, 4, -8, -3, -5, -1, 7, 0], [13, -1, -3, -2, 5, -3, 4, 3, 5, 1, 6, 3, -3, 5], [-9, -1, -1, -2, 8, 2, -1, 5, 2, 4, 5, -3, 0, -7], [-5, 4, 2, 3, -7, -5, 1, -9, -1, 7, -1, 3, -1, -5], [-13, -1, 1, -2, -2, 2, 1, -6, 0, 4, 0, -2, -4, -6], [-15, 3, -1, -5, 11, 1, -1, 0, 8, 5, 7, -3, -9, -2], [-2, -10, -1, 3, 2, 7, -5, 7, 1, -2, -5, -5, 1, -3], [2, -6, 4, 13, 0, 3, -1, -3, -2, -4, -2, -5, 3, 1], [10, 4, 0, 2, -6, -2, -2, 3, 4, -1, -3, -5, 1, 0], [10, 6, 5, 5, -3, 0, 3, -5, 0, -1, -1, 0, 6, 2], [4, -7, 5, 1, -1, -1, 1, -6, 0, 7, -2, -1, -2, 1], [-5, -1, 9, 4, 10, 14, -11, 3, 2, -9, 1, -12, -5, -7], [-8, -2, 0, -4, -2, 2, 2, -6, -5, 3, -4, 7, 1, 1], [-1, 7, 0, -4, 8, -4, 6, 8, 6, -2, -4, 5, 3, 2], [-1, 7, -7, -8, 0, -7, 5, -3, 3, 2, 1, 9, 0, 1], [3, -2, -4, -2, 3, 0, 1, 5, 8, 0, -4, 4, -1, -3], [-8, 2, -6, -1, -1, 1, 2, 1, 0, -4, 0, 3, 4, 1], [12, 4, -4, -5, 2, -7, 9, -1, -1, 2, -4, 6, 3, 4], [-7, 0, 0, 6, -6, 0, 5, 6, 0, 6, -8, 12, 8, 4], [12, 2, -4, -1, -5, -8, 8, 8, 11, 4, -7, 6, 2, 4], [16, -5, 1, 7, -12, 1, -4, -1, -6, -5, 6, -6, 1, -1], [-10, 13, -2, -9, 4, 1, 0, 9, 6, -3, -1, 4, -2, -3], [-14, -5, -5, 4, -3, 2, 0, 0, 7, 3, 3, 4, 0, -2], [-1, -6, 1, 3, 7, 3, -5, -6, -10, -3, 8, -1, -1, 4], [-4, -4, 8, 7, -1, 3, 2, -1, 3, 0, 15, -3, -3, -1], [5, 9, -2, -8, -2, -8, 3, -7, 2, 2, 4, 2, 1, 2], [1, -14, 2, 6, 7, 1, 3, 5, 0, 6, -4, 0, -3, 1], [1, -7, -1, 3, 11, 3, -3, 5, -5, -5, -1, -9, 0, 5], [-3, -5, 3, 1, -2, 3, 1, -7, -6, -1, -2, -5, 5, 1], [-11, 3, -3, 4, -5, 4, 2, -5, -7, -3, 0, 9, 4, 4], [-1, -3, -1, 1, 5, 9, -6, -3, 1, -7, -2, -2, -7, -3], [-4, -8, 0, -3, -6, -3, 4, 0, 4, 4, 2, 4, 0, -2], [-21, -11, -1, 0, 16, 1, 2, 10, 10, 3, 1, -3, -5, 3], [-4, 1, -3, 1, 4, -7, -4, 1, -5, 1, -1, 2, 1, 6], [27, -6, 2, 0, 2, 0, 7, 0, 5, 9, -2, 7, 1, -2], [0, -4, -2, -4, 10, 1, 3, 5, 8, -5, 1, 0, 2, 1], [6, 0, -1, -3, 8, -3, 7, 3, 7, 4, 5, 6, 1, 1], [3, -5, 8, 1, 10, 7, -2, 4, -6, 0, 4, -6, -2, -3], [3, 9, 5, 3, -14, -4, -1, -16, -11, 1, 4, 0, 1, -1], [-6, -4, 0, 2, -6, 12, -3, 2, 5, -2, -1, 3, -4, -8], [-2, -4, 0, 1, -7, -3, 4, -2, -1, 2, -4, -2, -3, -3], [7, -4, 6, -3, 2, 5, 0, -1, 5, -5, 9, 1, -2, -1], [-23, 10, -4, 3, -3, -3, 3, 0, -10, 0, 1, 4, 5, 6], [-12, 1, 1, 0, 4, 6, 2, 3, 1, 3, 2, 0, 4, -3], [-10, 13, 0, -2, 2, -1, 1, 0, -6, 2, -1, 9, 7, 7], [-11, -1, 1, 1, -4, -7, 2, -6, -10, 6, -2, -3, 2, 2], [3, 0, 2, 3, 0, 3, -4, 2, -11, -6, 0, -1, 1, 3], [-2, 10, -8, -9, 5, -4, -1, -3, -2, -1, 9, 6, -1, 2], [9, 9, -1, -11, -5, -5, 0, -7, -2, -2, 1, 3, -1, 0], [-6, -1, 5, -10, -2, -4, 4, -9, -3, 4, -2, 0, 2, -1], [0, -7, 3, 3, 2, -1, 6, -6, -2, 4, 0, -2, -5, 2], [-7, -3, 0, 3, -11, -3, -3, -8, -2, 3, -1, -4, -7, -3], [5, 7, 3, -8, 3, -2, -5, -3, -2, 0, 6, 0, -1, -5], [3, -3, -2, 0, 2, 0, -4, 5, 9, -1, 0, -5, -2, 5], [2, -11, 3, 2, 1, -2, 4, -1, -5, 2, 4, 2, 5, 5], [-7, -4, -12, 5, 3, -2, 4, 10, 9, 1, 6, 5, 4, 4], [8, -8, 4, -5, 7, 9, -5, 6, 0, -5, -1, -5, -6, -7], [9, -10, 4, 2, 1, 4, 3, 1, 6, 3, -3, -2, 1, 2], [-18, 2, 2, -6, -1, 6, -1, -9, -8, -4, 1, -5, -2, -2], [34, 2, 1, -2, -6, 2, -3, 1, -1, -5, 8, -2, -2, 0], [7, -5, 7, -1, 3, 9, 1, -2, 1, -8, -4, 0, -5, -7], [8, 2, -6, 0, 4, -4, -6, 9, 5, 3, 1, 4, -2, 5], [-9, 13, 1, 3, -7, -1, -3, -1, -7, 1, 2, 0, 0, 3], [10, 2, -4, -1, -7, -7, 1, -4, 3, 5, 8, 6, 2, 4], [-4, -7, -3, -5, -9, -1, -4, 1, -3, -5, -2, -3, 0, -5], [-3, -6, -6, 5, -8, -3, -6, -1, 0, 0, 1, 3, -3, -1], [34, -10, -2, 9, -5, 5, 2, 12, 10, -5, -6, 3, 6, 0], [-4, 3, -5, 0, 1, 8, -5, 5, -5, -2, -1, -2, -1, -3], [1, -6, -2, 3, -10, 4, -7, -4, -12, -6, -5, -5, 1, -2], [10, -3, 1, 3, -3, 3, 0, 5, 1, 1, 1, -3, -1, 0], [13, 0, -8, -1, -2, -3, -2, 6, 3, 3, -12, -1, 1, 0], [15, -6, 3, 11, 5, 11, -3, -1, -3, -6, 7, -3, -3, 2], [-15, 7, 7, 8, -5, 6, -8, 1, -5, -5, 9, -5, 2, -2], [26, -7, 7, 7, 6, 1, 8, -1, 0, 9, -3, 4, 3, 1], [-22, 2, -10, -1, -4, 1, -4, 2, -4, -5, 3, 7, 5, 5], [13, -1, 5, 3, -11, 1, 3, -11, -2, 9, 1, -1, -3, -3], [-4, 9, -1, -10, -3, 1, 0, -6, -8, -6, -10, 0, 0, 0], [-14, -2, 8, -2, 5, 0, 2, -9, 4, 1, 7, -4, -7, -4], [-12, -4, 0, 3, -4, 5, -8, -2, 1, -3, -5, -9, -4, -5], [12, 13, -2, -5, -7, -10, -1, -12, -8, -3, 1, 2, -1, -3], [9, 0, 0, -4, -5, -4, -1, 2, 1, 1, -15, 0, 0, -7], [-7, 1, -2, 3, -12, -9, 1, -8, -10, 4, -9, 3, 7, 7], [32, -7, 5, 0, -6, -3, 6, -8, -7, -3, -4, -5, 1, 2], [10, 0, -4, 13, -4, 3, -3, 1, 0, -8, 4, -6, -1, 3], [6, -3, 1, 8, -3, 3, -4, 7, 3, -2, -1, -5, 6, 2], [-4, -9, 5, 3, -6, 2, -2, 0, 0, -3, -2, -2, -1, -7], [-1, 2, 4, -2, 3, 0, 2, 3, 5, -2, 3, -6, -1, 2], [-6, -5, 1, 4, 1, -4, 4, -9, -1, 3, 4, 2, -1, 6], [-2, -10, 2, 6, 4, 11, -6, 2, -1, -1, 5, -6, 1, -5], [-4, 7, -9, -10, -2, -2, -2, 1, 3, 0, -2, 11, 2, 0], [9, -8, 4, -3, 3, 2, -6, 0, -7, 5, -2, 0, 2, -5], [-23, 4, -6, 9, 3, 9, -2, 7, 3, -5, 4, 4, 4, 7], [-8, -1, -6, 1, -1, -1, -1, -2, -2, -2, -9, 0, -1, 0], [-12, -6, 7, 14, -6, -2, -1, -9, -4, 7, -2, -6, -3, -2], [18, 8, -8, -4, -7, -9, 2, 2, 4, 4, -7, 4, 5, 8], [-10, -1, 9, -3, 0, 3, 1, -18, -5, -3, 0, -4, -8, -7], [-4, 10, -5, 6, 1, -6, 2, 7, 1, 3, 2, 4, 6, 11], [6, 2, -8, -5, 5, 0, -4, 3, 2, -2, 4, 0, 3, 3], [19, -4, -2, 2, 6, 6, -1, 9, 9, -4, 0, -5, 1, 9], [22, 5, 1, 0, -19, -8, 4, -9, -6, 10, -10, 3, -1, 3], [-14, 3, -1, -2, 10, 0, 2, 5, 2, 0, 4, -2, -10, -5], [-19, -4, 4, 4, 13, 4, 4, 9, 1, 4, 7, -3, 3, -3], [4, -3, -2, 0, -3, 6, -4, -4, 10, -9, 4, 1, -4, -4], [-22, 8, 2, 2, -16, -4, 0, -8, -7, -5, -10, 2, 8, 2], [-24, 0, 8, -2, 1, 0, -8, -7, -4, -6, 16, -6, -9, -4], [7, 0, -6, 5, -1, -2, -1, 0, 8, 0, -3, 5, 2, 5], [-6, 7, -7, -2, 3, -6, 0, 8, 7, 0, 1, 1, -4, 2]];
    aps := ConvertToHeckeField(raw_aps);
    chi := MakeCharacter_6024_a_Hecke(Universe(aps));
    return ExtendMultiplicatively(weight, aps, chi);
end function;


// To make the newform (type ModFrm), type "MakeNewformModFrm_6024_2_a_p();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose lines below.
// The precision argument determines an initial guess on how many Fourier coefficients to use.
// This guess is increased enough to uniquely determine the newform.
function MakeNewformModFrm_6024_2_a_p(:prec:=14)
    chi := MakeCharacter_6024_a();
    f_vec := qexpCoeffs();
    Kf := Universe(f_vec);
    // SetVerbose("ModularForms", true);
    // SetVerbose("ModularSymbols", true);
    S := CuspidalSubspace(ModularForms(chi, 2));
    S := BaseChange(S, Kf);
    maxprec := NextPrime(2999) - 1;
    while true do
        trunc_vec := Vector(Kf, [0] cat [f_vec[i]: i in [1..prec]]);
        B := Basis(S, prec + 1);
        S_basismat := Matrix([AbsEltseq(g): g in B]);
        if Rank(S_basismat) eq Min(NumberOfRows(S_basismat), NumberOfColumns(S_basismat)) then
            S_basismat := ChangeRing(S_basismat,Kf);
            f_lincom := Solution(S_basismat,trunc_vec);
            f := &+[f_lincom[i]*Basis(S)[i] : i in [1..#Basis(S)]];
            return f;
        end if;
        error if prec eq maxprec, "Unable to distinguish newform within newspace";
        prec := Min(Ceiling(1.25 * prec), maxprec);
    end while;
end function;


// To make the Hecke irreducible modular symbols subspace (type ModSym)
// containing the newform, type "MakeNewformModSym_6024_2_a_p();".
// This may take a long time!  To see verbose output, uncomment the SetVerbose line below.
// The default sign is -1.  You can change this with the optional parameter "sign".
function MakeNewformModSym_6024_2_a_p( : sign := -1)
    R<x> := PolynomialRing(Rationals());
    chi := MakeCharacter_6024_a();
    // SetVerbose("ModularSymbols", true);
    Snew := NewSubspace(CuspidalSubspace(ModularSymbols(chi,2,sign)));
    Vf := Kernel([<5,R![-3364, -22140, -13761, 67298, 10892, -53458, -1300, 17652, -863, -2796, 280, 210, -29, -6, 1]>,<7,R![432, 10592, 74828, 111196, -67332, -102972, 37177, 30681, -10497, -3477, 1199, 169, -58, -3, 1]>],Snew);
    return Vf;
end function;